On the face of it, normative conflicts are commonplace. Yet standard deontic logic declares them to be logically impossible. That prompts the question, What are the proper principles of normative reasoning if such conflicts are possible? This paper examines several alternatives that have been proposed for a logic of 'ought' that can accommodate normative conflicts, and finds all of them unsatisfactory as measured against three criteria of adequacy. It then introduces a new logic that does meet all three criteria, and (...) so allows for the possibility of genuine normative conflicts. (shrink)

This multiplex semantics incorporates multiple relations of deontic accessibility or multiple preference rankings on alternative worlds to represent distinct normative standards. This provides a convenient framework for deontic logic that allows conflicts of obligation, due either to conflicts between normative standards or to incoherence within a single standard. With the multiplex structures, two general senses of "ought" may be distinguished, an indefinite sense under which something is obligatory when it is enjoined by some normative standard and a core sense for (...) when something is enjoined by all normative standards. Multiple normative standards may themselves be given a preferential order; this leads to a concept of ranked obligation. This paper presents the foundations of this multiplex semantics and the propositional deontic logics they define. (shrink)

This volume presents a definitive introduction to twenty core areas of philosophical logic including classical logic, modal logic, alternative logics and close examinations of key logical concepts.

This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the (...) Routley-Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable. (shrink)

Combinator logics are a broad family of substructual logics that are formed by extending the basic relevant logic B with axioms that correspond closely to the reduction rules of proper combinators in combinatory logic. In the Routley-Meyer relational semantics for relevant logic each such combinator logic is characterized by the class of frames that meet a first-order condition that also directly corresponds to the same combinator's reduction rule. A second family of logics is also introduced that extends B with the (...) addition of propositional constants that correspond to combinators. These are characterized by relational frames that meet first-order conditions that reflect the structures of the combinators themselves. (shrink)

Deontic logic ought to be fundamental to ethical theory and the theory of practical reasoning, but, for various reasons, it hasn’t been. James Forrester faults the standard systems themselves; so, in place of standard deontic logic, he proposes a new deontic logic that should, he thinks, serve moral philosophy more adequately.

In 1926, Mally presented the first formal system of deontic logic. His system had several consequences which Mally regarded as surprising but defensible. It also, however, has the consequence that A is obligatory if and only if A is the case, which is unacceptable from the point of view of any reasonable deontic logic. We describe Mally's system and discuss how it might reasonably be repaired.

The relevant modal logic G is a simple extension of the logic RT, the relevant counterpart of the familiar classically based system T. Using the Routley-Meyer semantics for relevant modal logics, this paper proves three main results regarding G: (i) G is semantically complete, but only with a non-standard interpretation of necessity. From this, however, other nice properties follow. (ii) With a standard interpretation of necessity, G is semantically incomplete; there is no class of frames that characterizes G. (iii) The (...) class of frames for G characterizes the classically based logic T. (shrink)

The results of this paper extend some of the intimate relations that are known to obtain between combinatory logic and certain substructural logics to establish a general characterization theorem that applies to a very broad family of such logics. In particular, I demonstrate that, for every combinator X, if LX is the logic that results by adding the set of types assigned to X (in an appropriate type assignment system, TAS) as axioms to the basic positive relevant logic B∘T, then (...) LX is sound and complete with respect to the class of frames in the Routley-Meyer relational semantics for relevant and substructural logics that meet a first-order condition that corresponds in a very direct way to the structure of the combinator X itself. (shrink)

What is philosophical logic? Philosophical logic is philosophy that is logic, and logic that is philosophy. It is where philosophy and logic come together and become one. Philosophical logic is not a special kind of logic, some species distinct from mathematical logic, symbolic logic, formal logic, informal logic, modern logic, ancient logic, or logic with any other familiar modifier. There is only logic. Logic is the theory of consequence relations, of valid inferences. As such, it can be investigated and presented (...) in many ways, although the mathematical methods of modern formal or symbolic logic have proved extraordinarily fruitful. (shrink)

The method of supervaluations offers an elegant procedure by which semantic theory can come to terms with sentences that, for one reason or another, lack truth-value. I argue, however, that this method rests on a fundamental mistake, and so is unsuitable for semantics. The method of supervaluations, I argue, assigns semantic values to sentences based not on the semantic values of their components, but on the values of other, perhaps homophonic, but nevertheless distinct, expressions. That is because supervaluations are generated (...) from classical valuations which necessarily require reinterpreting the component expressions, but the reinterpretation of an expression is tantamount to the introduction of a new expression, or alternatively, to a shift to an entirely new language. To confuse the expression of the language for which a semantic theory is developed with its reinterpreted counterpart, is to commit a fallacy of equivocation. That is the flaw within the method of supervaluations. We see it manifest in a number of examples. (shrink)

Deontic logic ought to be fundamental to ethical theory and the theory of practical reasoning, but, for various reasons, it hasn’t been. James Forrester faults the standard systems themselves; so, in place of standard deontic logic, he proposes a new deontic logic that should, he thinks, serve moral philosophy more adequately.